Introduction to the Mathematics of Music (AK Peters/CRC Recreational Mathematics Series)

Introduction to the Mathematics of Music is aimed at helping bridge the substantial gap between a classical musician culture and the universe of mathematical notions in music.It explains the necessary notions, starting from scratch, with rigour but without any unnecessary formalism.It was developed from a course given in Perpignan, France, for a bachelor in Music theory. After a mandatory outline of the seminal role of numbers in music, based on the equations of consonance, the book introduces the essential formalisation of pitch-classes and pc-sets as elements and subsets of the integers modulo 12. Transpositions and inversions, traditional musical operations, are formalized in that context.Symmetries and structures are studied efficiently with these tools - for instance linking Olivier Messiaen’s forgotten Modes of Limited Transposition with subgroups of the dihedral group D12. The book ends with a sampling of the geometrical models of musical spaces that mark the modern era in the d